Some oscillatory singular integrals on Herz-type spaces. II (Q1862805)

The authors prove that some oscillatory singular integral operators of non-convolution type with non-polynomial phases are bounded from the Herz-type Hardy spaces to the Herz spaces and from the Hardy spaces associated with the Beurling algebras to the Beurling algebras in higher dimensions, even though it is known that in the classical case these operators are not bounded from the Hardy space \(H^1\) into the Lebesgue space \(L^1\). The results are generalizations of authors' previous results in the one-dimensional case [Yokohama Math. J. 47, 155-164 (2000; Zbl 0976.42008)].